[HDU 2255]奔小康赚大钱[KM算法]

#include<cstdio>
#include<cstring>
#include<iostream>
using namespace std;

const int INF = 0x7f7f7f7f;
const int MAXN = 311;

int n, nx, ny;
int match[MAXN], lx[MAXN], ly[MAXN], slack[MAXN]; // lx[]左标杆 ly[]右标杆 slack[]松弛量
int visx[MAXN], visy[MAXN], w[MAXN][MAXN];

int dfs(int x)
{
visx[x] = 1;
for (int y = 1; y <= ny; ++y)
{
if (visy[y]) continue;
int temp = lx[x] + ly[y] - w[x][y];
if (temp == 0)
{
visy[y] = 1;
if (match[y] == -1 || dfs(match[y]))
{
match[y] = x;
return 1;
}
}
else if (slack[y] > temp) slack[y] = temp;
}
return 0;
}

int KM()
{
// 1.initialize
int i, j;
memset(match, -1, sizeof match);
memset(ly, 0, sizeof ly);
for (i = 1; i <= nx; ++i)
for (j = 1, lx[i] = -INF; j <= ny; ++j)
if (w[i][j] > lx[i]) lx[i] = w[i][j];

// 2.find
for (int x = 1; x <= nx; ++x)
{
for (i = 1; i <= ny; ++i) slack[i] = INF;
while (1)
{
memset(visx, 0, sizeof visx);
memset(visy, 0, sizeof visy);
if (dfs(x)) break;

// 能到达这一步，说明再也挪不到新边给x了，所以要进行增广，增加新边来选择
int d = INF;
// 没有匹配的y，且两者有边相连
for (i = 1; i <= ny; ++i) if (!visy[i] && d > slack[i])
d = slack[i];
for (i = 1; i <= nx; ++i) if (visx[i]) lx[i] -= d;
for (i = 1; i <= ny; ++i)
{
if (visy[i]) ly[i] += d;
else slack[i] -= d; // 更改松弛量
}                       // 本来这些点是要松弛D的，结果已经松弛了d，那么之后如果要松弛只用松弛D - d就行了
}
}

int ret = 0;
for (i = 1; i <= ny; ++i)
if (match[i] != -1) ret += w[match[i]][i];
return ret;
}

int main()
{
int n;
while (~scanf("%d", &n))
{
nx = ny = n;
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= n; ++j)
scanf("%d", &w[i][j]);
printf("%d\n", KM());
}
return 0;
}